15.2 Born-Haber Cycle15.2.1 Define and apply the terms lattice enthalpy, and electron

affinity 15.2.2 Explain how the relative sizes and the charges of ions

affect the lattice enthalpies of different ionic compounds The relative value of the theoretical lattice enthalpy

increases with higher ionic charge and smaller ionic radius due to increased attractive forces

15.2.3 Construct a Born-Haber cycle for group 1 and 2 oxides and chlorides and use it to calculate the enthalpy change

15.2.4 Discuss the difference between theoretical and experimental lattice enthalpy values of ionic compounds in terms of their covalent character.

Born-Haber Cycle

A series of hypothetical steps and their enthalpy changes needed to convert elements to an ionic compound and devised to calculate the lattice energy.

Using Hess’s law as a means to calculate the formation of ionic compounds

Born-Haber Cycle Steps

1. Elements (standard state) converted into gaseous atoms

2. Losing or gaining electrons to form cations and anions

3. Combining gaseous anions and cations to form a solid ionic compound

Step 1: Atomisation

The standard enthalpy change of atomisation is the ΔH required to produce one mole of gaseous atoms

Na(s) Na(g) ΔHoat = +109 kJmol-1

NOTE: for diatomic gaseous elements, Cl2, ΔHo

at is equal to half the bond energy (enthalpy)

Cl2(g) Cl(g) ΔHoat = ½ E (Cl-Cl)

ΔHoat = ½ (+242 )

ΔHoat = +121 kJmol-1

Step 2: Formation of gaseous ions

Electron Affinity Enthalpy change when one mole of

gaseous atoms or anions gains electrons to form a mole of negatively charged gaseous ions.

Cl(g) + e- Cl-(g) ΔHo = -364 kJmol-1 For most atoms = exothermic, but gaining

a 2nd electron is endothermic due to the repulsion between the anion and the electron

Becoming cations

Ionisation energy Enthalpy change for one mole of a

gaseous element or cation to lose electrons to form a mole of positively charged gaseous ions

Na(g) Na+(g) + e- IE1= +494 kJmol-1

Lattice Enthalpy

Energy required to convert one mole of the solid compound into gaseous ions.

NaCl (s) Na+(g) + Cl-(g) ΔHolat

= +771kJmol-1

It is highly endothermic We cannot directly calculate ΔHo

lat , but values are obtained indirectly through Hess’s law for the formation of the ionic compound

Calculations Calculate the lattice energy of NaCl(s)

using the following: (kJmol-1) Enthalpy of formation of NaCl = - 411 Enthalpy of atomisation of Na = +109 Enthalpy of atomisation of Cl = +121 Electron affinity of Cl = - 364 Ionisation energy of Na = + 494

Enthalpy of atomisation + electron affinity + ionisation = enthalpy of formation + lattice energy

Magnitude of Lattice enthalpy

The greater the charge on the ions, the greater the electrostatic attraction and hence the greater the lattice enthalpy

Ex: Mg2+ > Na+

The larger the ions, then the greater the separation of the charges and the lower the lattice enthalpy

VICE VERSA

Trends

ΔHolat Change from NaCl

MgO 3889 Increased ionic charge

NaCl 771 ------

KBr 670 Larger ions

Use of Born-Haber Cycles

Empirical value of ΔHolat is found using

Born-Haber cycle. Theoretical value of ΔHo

lat can be found by summing the electrostatic attractive and repulsive forces between the ions in the crystal lattice.

Compound Empirical value Theoretical value

NaCl 771 766

KBr 670 667

KI 632 631

AgCl 905 770

Agreement Usually there is good agreement

between empirical and theoretical values If there isn’t good agreement

Implying that the description of the compound as ionic is inappropriate

There could be a significant degree of covalent character in the bonding (EN difference less than 1.7)

Presence of covalent character leads to an increase in ΔHo

lat